Conference Agenda

In this talk the focus is on copula-based procedures for testing whether a finite collection of continuous random vectors is mutually independent. In particular, we look into the class of meta-elliptical copulas and test the hypothesis whether the copula correlation matrix is a block diagonal matrix. The test statistic is a Phi-dependence measure of a rank-based correlation matrix estimator, whose asymptotic distribution under the null is obtained for general (Phi) functions and general elliptical generators. In case of the Gaussian copula, we also develop asymptotics when optimal transport dependence measures are used for testing the null hypothesis of independent random vectors. Some numerical studies, including comparisons with existing methods, are reported on.

Irène Gijbels, Steven De Keyser

University of Leuven (KU Leuven), Belgium.

The pair-copula Bayesian Networks (PCBN) are graphical models composed of a directed acyclic graph (DAG) that represents (conditional) independence in a joint distribution. The nodes of the DAG are associated with marginal densities, and arcs are assigned with bivariate (conditional) copulas following a prescribed collection of parental orders. The choice of marginal densities and copulas is unconstrained. However, the simulation and inference of a PCBN model may necessitate possibly high-dimensional integration.
We present the full characterization of DAGs that do not require any integration for density evaluation or simulations. Furthermore, we propose an algorithm that can find all possible parental orders that do not lead to (expensive) integration. Finally, we show the asymptotic normality of estimators of PCBN models using stepwise estimating equations. Such estimators can be computed effectively if the PCBN does not require integration. A simulation study shows the good finite-sample properties of our estimators.

Missing values in multivariate dependent data are common in many applied settings and pose challenges for standard imputation methods, particularly when complex dependence structures are present. We introduce NPCoImp, a nonparametric copula-based approach for imputing multivariate missing data. The method relies on the empirical beta copula to estimate conditional distribution functions of missing variables given the observed ones, allowing the imputation process to account for the radial symmetry or asymmetry of the joint dependence structure. NPCoImp is highly flexible and can accommodate arbitrary missingness patterns in multivariate settings. We assess its performance through an extensive Monte Carlo simulation study, comparing it with classical imputation methods, the CoImp algorithm, and the machine-learning-based missForest approach. The results show that NPCoImp performs particularly well in preserving dependence structures across different sample sizes, missingness levels, and dependence strengths. The practical relevance of the method is illustrated through applications to real data from the agricultural sector.

We introduce a new dependence order, termed the conditional convex order, whose minimal and maximal elements characterize independence and perfect dependence. Moreover, it characterizes conditional independence, satisfies information monotonicity, and exhibits several invariance properties. Consequently, it is an ordering for the strength of functional dependence of a random variable Y on a random vector X. As we show, various recently studied dependence measures---including Chatterjee's rank correlation, Wasserstein correlations, and rearranged dependence measures---are increasing in this order and inherit their fundamental properties from it. We characterize the conditional convex order by the Schur order and by the concordance order, and we verify it in settings such as additive error models, the multivariate normal distribution, and various copula-based models. Our results offer a unified perspective on the behavior of dependence measures across statistical models.